The Anderson-Darling test is a statistical method used to determine whether a data sample is likely drawn from a specific theoretical distribution. Unlike parametric tests, it does not require assumptions about specific parameters of the distribution. Instead, it compares the sample's empirical cumulative distribution function (ECDF) with the cumulative distribution function (CDF) of the hypothesized distribution. Critical values for the test are specific to the chosen distribution rather than...

When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...

Standardized test scores often follow a symmetric distribution that can be modeled with the normal distribution, a fundamental concept in statistics. This distribution is particularly useful for interpreting test performance fairly across populations, as it provides a mathematical framework for understanding variability and central tendency in large datasets.From Histogram to Frequency DistributionRaw test data are often displayed using histograms, where the height of each bar represents the...

A complete procedure of testing the hypothesis about a population mean is explained here.
Estimating a population mean requires the samples to be distributed normally. The data should be collected from the randomly selected samples having no sampling bias. The sample size needed to be higher than 30, and most importantly, the population standard deviation should be already known.
In most realistic situations, the population standard deviation is often unknown, but in rare circumstances, when it...

The goodness-of-fit test is a type of hypothesis test which determines whether the data "fits" a particular distribution. For example, one may suspect that some anonymous data may fit a binomial distribution. A chi-square test (meaning the distribution for the hypothesis test is chi-square) can be used to determine if there is a fit. The null and alternative hypotheses may be written in sentences or stated as equations or inequalities. The test statistic for a goodness-of-fit test is given as...

A complete procedure of testing a hypothesis about a population mean when the population standard deviation is unknown is explained here.
Estimating a population mean requires the samples to be approximately normally distributed. The data should be collected from the randomly selected samples having no sampling bias. There is no specific requirement for sample size. But if the sample size is less than 30, and we don't know the population standard deviation, a different approach is used; instead...